I'm building a world that happens to be flat. Well, it has hills and mountains, but no curvature.

However, I still want to limit the eyesight to a few kilometers even if there are no hills around. I don't really care if towers/mountains allow you to watch further (though it would be a nice bonus). Basically, I want the world to be like ours at first glance.

A few informations on my world:

People are mostly humanoid, no height difference.

The setting is medieval, no pollution.

The world was designed by gods who can do any magic they want, though they want to minimize their impact.

Preferably, an eyeglass should allow you to see further.

I would like to avoid (if possible) biological alterations/curse.

Luminiferous aether is totally a thing in my world, no physics after the Michelson–Morley experiment can be considered to be valid.

There are no time zones (flat earth remember).

I don't care what happens on the borders of the world, it is approximately the area of Europe and most of what happens will be on the center.

$\begingroup$with a flat earth, you are using your own physics anyway, so why not just operate under the assumption that greater Rayleigh scattering of light? The atmosphere just obscures anything at significant distance - it all just blends into a uniform haze by the time you get several kilometers out. Nothing significant needed here at all, and just go with it - don't bother trying to explain it in detail, it just is (I cannot imagine a medieval fantasy book enjoyably going into talking about the minutia of optics).$\endgroup$
– pluckedkiwiJan 31 '17 at 16:16

$\begingroup$No time zones? Is there day and night? Does the sun seem to move across the sky?$\endgroup$
– WillkJan 31 '17 at 16:17

$\begingroup$@pluckedkiwi If I eventually write and publish, maybe there will be a medieval fantasy book enjoyably going into talking about the minutia of optics.$\endgroup$
– PatJJan 31 '17 at 16:18

12 Answers
12

If you're trying to get a geometric effect without actually having the geometry to cause it, it can be a bit tricky. Consider having photons not move in a straight line. If photons are affected by gravity, they could curve down towards your flat earth. Of course, you have to worry about whether the photons can escape the sun, but if you're not even concerned with the boundaries of the world, getting photons from the sun should be a reasonable level of handwaving for your gods to put forth.

Having an eyeglass let you see further past the horizon is trickier, because that doesn't even work with a real horizon. To make that work, you may need to create a ray tracing world. Instead of having light from the sun hit everything an bounce off it, sensors of light (i.e. eyeballs) emit rays in the opposite direction. Everything which those rays hit also act like sensors, sending off rays in all directions until a ray hits a light source. This is how we render 3d graphics in a lot of cases. Doing this would permit your eyeglass to change the nature of the reverse-photons, letting them go further before they hit the ground.

$\begingroup$If photons are affected by gravity and curve downwards, the people would initially believe that they lived in a bowl. All parts of the world would be visible from any location. - The heliograph might be developed before the alphabet, and the first writing would be heliography transcription.$\endgroup$
– A. I. BreveleriFeb 2 '17 at 19:42

$\begingroup$Adding A.I.'s comment, that's pretty much what I want. Is it ok to edit the question to take this into account?$\endgroup$
– PatJFeb 13 '17 at 13:07

Actually, for the most part, your world should look like Earth at first glance, because Earth looks flats from its surface. You'll only notice its curvature if you're looking at a ship a long way away at sea, for example. It says here that

You should be able to detect [the curvature] from an aeroplane at a cruising height
of around 10,600 metres (35,000 feet), but you need a fairly wide
field of view (ie 60 degrees) and a virtually cloud-free horizon. The
reality is that clouds, hills and mountains mean we rarely get to see
the kind of perfectly flat horizon where the curve would be most
obvious.

Even at the top of Everest you won't be able to see the curvature of Earth. So that shouldn't be a problem. The real problem is looking at ever increasing distances and not bumping into any hard limit.

On a flat Earth, in theory, you could see as far as you wanted provided you had a sufficiently powerful eyeglass. In practice this would be limited by Rayleigh scattering. If that's not enough, there could be a neverending storm front at the border of the world blocking the view. Or a circular waterfall going all around the world and feeding a circular river or sea. Since you're making up the physics, it's your call. I think you should make this boundary as interesting as possible and get it to work for the story.

I like the idea of inverting the "flat earth" model. Theologians argue that the evidence implies a spherical earth, but it's obviously, scientifically, flat. That's awesome.

It really comes down to what you mean by "flat."

If you mean a classical flat plane world, with a dome sky (like those old pictures), the easiest explanation is magic did it.

The creators didn't want humanity looking off into the distance under the sky and seeing the walls of the dome actually reaching down to the ground. To achieve this, they've slightly modified the physics of the world: physical light generally curves "down". Maybe light is affected by gravity at a much higher rate, or maybe the "ether" causes light to slow and "drop" like a canon ball through the air. In either case, sight lines would naturally be constrained to local space.

The stars, sun, and moon in the sky still "work" because their light streams down; there's no more "down" for the light to stream. Sunrises and sunsets are explained by the "tired light" struggling to reach the viewer.

Spyglasses still work too, but nobody knows why. The reason is that everything emitting light emits it in a "spray," and the optics in spyglasses allow you to see fainter light. So...

Note an interesting effect of "light spray." The more powerful the glass, the more "spray" you can collect and see a farther distance... but you can ALSO estimate distance based on the angle offset you have to look "up" to see a light source!

Another interesting effect would be that artillery and archery become even more of a specialist skill, as sight lines are no longer straight, which means that operators will need to use their judgement to offset shots not only for gravity and windage, but ALSO for the optical illusions of range. Magical weapons, perhaps, may have been created specifically to alleviate the problems of range. Or, perhaps, nobody bothers with long range weaponry, and all battles are fought with swords and fists.

Now, again, the point here was for the Gods to hide the seam between the sky-dome and the flat ground, so you've got a couple of options as you walk away from the center of your landmass.

The first is to pull a Truman Show, and have the skydome come down into the ocean. As long as nobody sails into the wall, nobody will know it's there.

Another option is to have the strength of the "curve down of light" increase as you move farther away from the center. As you get closer to the "edge" of the world, the world gradually gets darker and darker, as light emitted gets "pulled" or "dropped" to the ground faster and faster, until by the time you reach the wall it's literally pitch black (all light sources immediately fall to the ground). Combine that with a human fear of the dark, and you could easily discourage people from going too far.

$\begingroup$Great answer! My characters know they are on a flat world under a dome, and the gods are happy with that. Apart from that this is really the kind of answer I'm looking for.$\endgroup$
– PatJJan 31 '17 at 16:45

6

$\begingroup$Light curving down does not create a horizon, instead it creates the illusion of the world bending upwards and finally forming a wall. You should have the light rays bending up instead for a horizon illusion.$\endgroup$
– jknappenJan 31 '17 at 17:12

$\begingroup$@jknappen Great point! Also, that would mean that light is lighter than air, which makes perfect sense.$\endgroup$
– PatJJan 31 '17 at 18:04

$\begingroup$Light curving down should create an "observable universe." A photon emitted by something eventually strikes the ground; if you are not within the "observable universe" of that photon, as far as you are concerned, there is nothing there... therefore, a horizon (of sorts). It's not a horizon like a spherical earth, but objects "fade in" as they approach your "observable universe." Bright lights are visible from farther distances, so the Sun is still visible during sundown, but it gets dimmer as it approaches the horizon. I'm hurting wrapping my head around this, @jknappen.$\endgroup$
– Zoey BolesJan 31 '17 at 19:48

While our round Earth looks, it's possible that a flat earth will appear curved to its inhabitants. This effect would be due to the refraction of light as it passes through the atmosphere.

The simplest version of this atmospheric refraction model of a flat earth would be that this earth would curve upwards the further away from where a person was standing. It could be like standing in the centre of a bowl. Instead of a horizon everything in the distance would be effectively rising higher further it was from where you were situated.

Please this effect depends on the science of optics as it was developed before the Michelson-Morley experiment. This answer hasn't considered the influence of a luminiferous ether on the refraction effects, but the OP devised how the ether affects light in his world it will be easy to adjust his model accordingly and determine how a refraction bowl view of the flat earth might look.

Thermal differences in the atmosphere could create different degrees of refraction. Instead of uniformly curving upwards this could lead to a complicated affair curving both up and down in different places. This might be continually be rippling and undulating.

A flat earth might seem to be unstable and changing in unpredictable ways. Imagine the landscape curving away either up or down and possibly rippling as if it was the edge of the sea.

EDIT:

Please note the original answer had "diffraction" instead of "refraction" as the cause of the optic effects described above. This error has been fixed.

$\begingroup$I'm not sure I understand your answer, could you expand/vulgarize? Also, the surface of my earth is flat, but there is stuff under it to hold it together and avoid ripples (this will go in a future question btw).$\endgroup$
– PatJFeb 1 '17 at 17:14

$\begingroup$@PatJ. Think of mirages. The images of objects due to atmospheric refraction. Light paths are bent. Instead of seeing things in a straight line, they will appear to be where they are not. The apparent "horizon" can be higher or lower that where the observer is located. I assumed most likely this would be up, so the flat earth appears to curve upwards like a bowl. It could possibly curve downwards or its appearance could "ripple". This is purely due to the optics of refraction.$\endgroup$
– a4androidFeb 2 '17 at 1:07

$\begingroup$@PatJ. This seemed obvious to me, but I realize may not have been obvious to anyone else. All apparent curvature and rippling effects are purely optical distortions caused by refraction. The effect may not be uniform, hence the apparent ripples.$\endgroup$
– a4androidFeb 2 '17 at 1:14

$\begingroup$@PatJ I hadn't though of it before. But a flat earth might flex and bend, I've always assumed it would be stable like a rigid platter, and the whole flat-scape might ripple and undulate like a giant paper plate. It's a nicely surprising idea.$\endgroup$
– a4androidFeb 2 '17 at 1:20

When canoeing on a lake in Northern Saskatchewan, what you can see is effectively limited by the ability of light to travel through the atmosphere. At 2 miles trees blur into a solid mass. At 8 miles, you can tell land vs water. At 15 miles there are mirages of higher points of land.

One trip I had a set of binoculars with me. The lake was calm with only tiny wavelets.

It was 2 miles to the other shore. I handed a boy my binocs, and said, "Look at the far shore, and find something obvious right at the water's edge."

"Ok. Got it."

"Now squat down"

"Where did it go!"

Other kids came over to try it.

Took about 10 minutes for someone to come up with the idea that it was hiding behind the curve of the surface of the water. A 2 mile span has a 'bump' of water about 2.6 feet tall.

Still, this is a pretty subtle effect.

Things more noticeable:

On a round earth, ships start to vanish from the bottom up. You need to be above the ocean to see this. There is enough mist and haze just above the surface, that the boat blurs and vanishes. On Flatland going up in height would only increase the distance before it vanishes.

Mirage physics would be extended. Right now you can see mirages up to about 40 or 50 miles under optimum conditions. (cold to warm vertical gradient) On a flat earth, it would take a smaller temperature difference, and given clear air you would be able to see it further away. You could make a whole art out of sending temperature probes up from ships and from that figure out the probable light path, to figure out how far what you were seeing was away from you.

Does your world have tides? How does the sun work?

If a flat world is spinning, the water goes to the edge. A flat world that isn't spinning will won't have coriolis forces. No tornados, no hurricanes. No cyclonic storms. I'm not sure if there would be any wind, aside from convection cells -- essentially sea and land breezes. On earth the big wind driver is the combination that the equator gets about 2.5 times the insolation of the poles, coupled with it spinning.

If the sun is a fiery chariot flying close above the surface (say 1/4 of the NS dimension of the world, then you can establish a thermal gradient. Air would move toward the solar path, rise, and return at elevation. This would be modified by mountains, and oceans, but not by huge amounts.

Seasons would require a periodic movement of the path that Helios drove.

I'm really surprised that no-one understands perspective and in particular the mathematical concept of a limit.

Here's a non-mathematical explanation. Imagine an infinite flat earth with perfect visibility. Above it is an infinite flat sky that is parallel to the earth. The land won't go up forever and the sky won't go down forever (otherwise they would cross over). There will be a clear line where they meet. Where will the line be? It will be level with the observer's eyes.

You declared that there is Luminiferous ether in your scenario. Pre-relativistic physics can provide a good explanation for the existence of the horizon in the flat world:

Newtonian gravity does not affect light, since it has no mass, it is just a 'mechanical' wave propagating in the ether. But you can give the ether a downward pointing, constant velocity. (or the earth and all solid objects an upward pointing) If this velocity is comparable to the speed of light, all the lightrays will appear to follow a diagonally downwards pointed path, when observed from the flat Earth

The distance, at which you can look through varies with your angle of viewing, but has a well defined maximum, not by scattering and fading, but by colliding in the ground, just like with our spherical horizon.

Of course eyeglasses won't provide broader horizon. (just like they don't provide it on our Earth)

You can't see very far in water because light does not go very far into it. That's because it is more opaque than air.

Just the same, if you have a gas that is more opaque than our own world's air, it will constrain the distance from which objects can be seen more than regular air. But it won't be washed away by rain, like fog would.

The very best answer this site has ever seen (and which was unfairly shot down) posited that, on a flat Earth, the wall of ice that keeps oceans in place is kept in low temperatures due to the special flatulence of the elephants below the world disc. That flatulence may have other components, more volatile, which go over and above the ice wall and fill the world homogeneously. Those gases have no smell, and are breathablr, but have just the right opacity to constrain the horizon to whatever range you see fit.

That is also why the horizon gets farther when you climb a mountain, since gases will naturally have higher concentrations on lower altitudes.

A "Flat World" does not necessarily imply perfect planarity --- it's not a flat piece of wood upon which the gods have painted green and blue bits. Although, there may well be worlds exactly of that type.

As I understand it, your world consists of something like this:

The horizon for people inhabiting the edgeward regions, along the coasts, will largely consist of hazy air and pressure-variant water. Low pressure systems out at sea will cause the water level to rise and storm driven waves will further obscure the true horizon (the Edge itself). Gravitational effects of the Sun and Moons (stronger at the Edge) will also cause variations in general sea level. Most folks living in the lowland regions of Asia, down along the Red Sea, have something like a thousand miles of Ocean before their vision reaches the Edge. Atmospheric blurring, sea-sky melding (a quasi-mirage where atmosphere and ocean blur together as they meet in the far distance), haze, fog, distant storms, variations in sea level all contribute to the foreshortening of the horizon.

The peoples inhabiting the spindleward regions experience a completely different issue. Those living along the coasts of, for example, the Euxine Sea (just north of the rotational pole) in the regions of Trebizond live at sea level. To the south, their horizon will be the Galatian Mountains that rise up from the coastlands. Towards the east, west and north, their vision will contend with sea and will experience similar limitations to the Res Sea Asians: haze and atmospheric blurring. Beyond the Scythian Coast, the horizon will in fact be high points of the undulating steppes of Europe. Woodlands, hills and weather will limit how far they can see.

The maximal horizon will probably be seen by the high mountainmen of Hyperborea, who should be able to discern the faint line of the Edge, particularly at night where the curve of the world blots the stars beyond. They should also have spectacular Sunsets and Moonsets where the Edge becomes plainly visible. Of course, the atmosphere and weather will also play a role, but the advantage of living seven to ten thousand feet up can't be beat!

The Caucasian monks, living in the 20,000+ foot high Spindle (the ancient rotational pole, before centrifugal forces caused the land to slide around a bit), can probably make out the dim smudge of the coasts of the Red Sea because they can look out and over the undulating steppes of Asia. Again, haze, blurring and sea level will diminish the horizon even for them. To the east, they can surely see the forests of Massagaetia and Bactria beyond the Caspian Sea; but the highlands and low mountains that give rise to the Artaxes River will obscure anything further. The same view can be had to the north where the highlands of Scythia will be their horizon.

Something all answers seem to forget is simple geometry and the resolution capability of the human eye, but also telescopes..

Human eyesight is a frustum, with the back plane at infinity. But objects further away get smaller. At a certain distance, an object will be so small that the human eye simply can not longer distinguish it.

Which means at 1km away, you can not longer distinguish any objects below 0.3m.

Hubble can not resolve the lunar landers. Even with really powerful telescopes, it will not be possible to distinguish objects really far away. And we are talking about an unobstructed line of sight here. On a perfectly flat world, foreground object will inevitably obstruct bigger objects farther away. Imagine standing 100m behind a 100m high church. You will not be able to see a 200m high cathedral that is exactly 100m behind the church. Thats simply geometry.

A flat earth will already have a horizon. If you you look parallel to the ground, the horizon will run exactly horizontal at half height through your field of view. And you can see foreground objects (which will stick out atop the horizon), but background objects will all blend together into an indistinguishable mush of colors.

And that doesn't even include atmospheric effects. Fog, smoke, scattering. Shimmering air due to temperature differences. All those help obstructing the view well below infinite - actually rather much below infinity. You say no pollution, but in a medieval setting smoke from burning wood fires, especially in winter will have relatively thick smoke and obstruct the view.

If you want to lower how far people can see unaided, you simply lower their angular resolution or introduce hills & mountains, which act as natural sight barriers. Forests do as well, as do high buildings or fog.

https://en.wikipedia.org/wiki/Prisoners_of_Power
[...]The novel starts when Kammerer accidentally discovers an unexplored planet Saraksh inhabited by a humanoid race. The atmospheric conditions on Saraksh are such that the inhabitants believe that they live inside a sphere.[...]
Bonus: Would be great to produce the world, where people believe the planet is a sphere, when it's really flat.

$\begingroup$That's not what I want, but it's interesting.$\endgroup$
– PatJFeb 2 '17 at 16:36

$\begingroup$@PatJ, Sorry, I'm think you missunderstand me. I'm point you at some option using atmosphere condition, there ones vision is reflected, so at distance he saw the sky above, while looking horizontaly, this will produce illusion of a round planet around the observer, even if it's really flat. Strugatskys made it another way, their's observer was looking down, so observers mind get s illusion what he live inside the sphere, not outside of it.$\endgroup$
– mr4eshirFeb 6 '17 at 11:07

Thank you for your interest in this question.
Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).